Did you enter your full email address as the username for IMAP and SMTP (johnappleseed@icloud.com) or just the username? According to Apple's Documentation (https://support.apple.com/en-us/102525) the full email address must be used as the username.

Ben: I enter the full email address for the outgoing SMTP server, but just the username for the IMAP incoming server. But just to be sure, I have tried several times entering the full email address for both. This does not solve the problem.

I have new information: I have now also tried using Outlook on a brand new fresh Windows 11 Dell i7 laptop, and get a similar failure to login error. Also installed a fresh Thunderbird on this new laptop-- and get the same login error. (I did install iCloud for Windows first thing -- that works ok-- in case that's needed.) All my GMail accounts setup on the new laptop without any problem-- the problem is just with an iCloud custom domain email account.

So the only thing that works (for my iCloud custom domain mail account) is using Mail on iOS/iPhone. Thunderbird and Outlook under Windows (on two computers) both fail.

So given that *both* Thunderbird and Outlook fail to login, I am going to assume this is a not a Thunderbird problem per se. I don't know what/where the problem is, but will give up trying to fix this. Without network tools and skills, It's beyond my ability as a user. Right now I am in the process of deleting my custom domain, and will start over someday.

The first thing to consider is apple do not like using open standards for anything, Like Microsoft they offer all sorts of platitudes about innovation and customer needs. The reality is both love their walled garden where only what they sell works seamlessly with their other stuff.

Let's start simple and look for things that might be different. Does Thunderbird work as expected with your OS started in safe mode with Networking. Instructions for each operating system: Windows 10/11, Windows 8, Windows 7, OSX

If that did not get mail happening;

What is the custom domain? What do these guys report about it https://intodns.com/ Especially with regard to MX records, but generally

Then log an attempt to set up the account and report your results. https://thunderbirdtweaks.blogspot.com/2021/10/logging-new-account-wizard.html